OK, I think I have it pinned down.
Right now, the POV-Ray exporter invokes a file save dialog, while the other exporters don't.
I can see no reason for this difference. (The POV-Ray export is a bit different because it
must generate 2 files, but as far as I can see the code for that is independent of the call of
the dialog).
I've done a quick test changing code in ScriptEvaluator.java and now all of the exporters
raise a file save dialog (vrml, x3d, maya, and idtf whenever it gets a popup menu entry).
Saving jvxl isosurfaces does not, but I think it should too.
They are still offering by default the internal model name, not the root filename. I'll look into
that, but since you can choose/type the name you want, it is not so much of a trouble.
More tomorrow

Hello Robert
Thanks for reporting this.
I knew that the model's internal name was being used for the exported
filename, but none of us thought that would be a problem, as you have
now found. The error due to special characters will certainly have to
be taken care of; I'll see what I can do, or else it will have to be
a task of Bob's ;-)
(All this was, I think, carried over from duplicating the first
exporter, maybe Povray or the first Vrml. Actually, the Povray
exporter has a dialog; that's a line I can follow; more news on this
later on the day)
What we would actually need is a proper export dialog. That has being
mentioned once in the dev-list. But that needs someone willing to
code it (I most certainly cannot do that).
Maybe doing the export using the command line ("write" command) would
avoid your problems, since then you choose the filename as part of
the command.
As for the target folder, what you describe is just an effect of Java
standards; it uses the folder where Jmol.jar was run from, in the
case of the app. I'm not sure what the signed applet would do, but
likely the same, use the default Jmol directory.
Sorry for your trouble; it will lead Jmol in the best direction of
improvement,
though.

In converting a number of MOL files to WRL we found that the exported filename is
not using the filename from the original and changing the extension but rather using
the title found in the first line of the MOL file.
If that contains double or single quotes the export fails.
If it contains spaces, colons, left square barackets [ then the
exported filename is given as jmol.wrl (there may be other things
that affect it but these were what we saw in our 200 conversions).
No file menu is now given when doing the export and all the files
were placed in the Jmol/build directory from where we were running
the applet. Would using the signed applet have made any difference?
Thanks
Robert